New Criteria of Targeting Welfare in Italy: an Appraisal of the Distributive Effects
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Baldini, Massimo; Bosi, Paolo; Toso, Stefano Working Paper New Criteria of Targeting Welfare in Italy: an Appraisal of the Distributive Effects Quaderni - Working Paper DSE, No. 348 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Baldini, Massimo; Bosi, Paolo; Toso, Stefano (1999) : New Criteria of Targeting Welfare in Italy: an Appraisal of the Distributive Effects, Quaderni - Working Paper DSE, No. 348, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4961 This Version is available at: https://hdl.handle.net/10419/159189 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/
1 New Criteria of Targeting Welfare in Italy: an Appraisal of the Distributive Effects Massimo Baldini, Paolo Bosi, Stefano Toso* Index 1) Introduction 2) The Italian social assistance system 3) Old and new tests of means: an estimation of the distributive profiles 4) Towards a new framework for social assistance 5) Conclusions Appendix 1 Appendix 2 References 1. Introduction Means-tested social assistance programs have acquired, in the last two decades, an increasing role in the majority of industrialised countries. Although the issue of whether social assistance should be targeted or universally granted remains a main subject of dispute (Harding et al. 1994; Mitchell 1995; Smolensky et al. 1995; Atkinson 1995, 1998), the shift towards targeting is in practice quite widespread, mainly reflecting the wish to curb social security budgets in a general context of fiscal restraint. The issue of targeting welfare assumes a particular importance in Italy, whose social assistance programs resemble more the rudimentary regimes typical of Southern Europe than the evolved systems of other EU countries. Indeed, the Italian welfare system is characterised by a number of categorical schemes limited to aged and disabled people, a discretionary relief (mainly in kind) provided by regional and local governments, and the absence of a national minimum income scheme as a universal safety net. To tackle these severe shortcomings, an articulated plan of reform proposals has been put forward in a report issued in 1997 by a special governmental commission on social expenditure. Some of its proposals have recently found two important applications, the reform of means-testing criteria and the experimental introduction of a national safety net scheme, an absolute novelty for the Italian system. The strategy behind the reform is to increase assistance for those most in need and to ensure that public expenditure is better targeted. The paper deals with the distributive implications associated with this reform plan, and in particular with the new entitlement rules which have recently designed to establish the access to welfare expenditure. Section 2 critically reviews the Italian social assistance system and briefly describes the institutional design of the new targeting system, which will gradually substitute the tests of means currently applied. Using the micro-data contained in the most recent sample survey of household income and wealth conducted by the Bank of Italy1 and the tax-benefit microsimulation model Dirimod95, Section 2 also examines the sense in which the shortcomings mentioned above substantially undermine the effectiveness and efficiency of income support programs in alleviating poverty among Italian households. Section 3 is devoted to study how different economic and demographic groups of the population are likely to change their relative position if households are * Massimo Baldini and Stefano Toso: University of Bologna, Dipartimento di Scienze Economiche. Paolo Bosi: University of Modena and Reggio Emilia, Dipartimento di Economia Politica. E-mail: [email protected], [email protected], [email protected] . 1 See Brandolini 1998 for an extensive description of the Bank of Italy Survey.
2 ranked first by a variable representing old means-testing criteria, and then by the new test of means; this analysis aims to clarify how various groups are likely to change their relative probabilities to access social services. Section 4 evaluates the distributive impact of the new spending programs introduced with the budget law for 1999 and of some reforms of the whole assistance system which, although highly speculative, can shed some light on the likely direction towards which the Italian welfare state is evolving. Finally, Section 5 concludes. 2. The Italian social assistance system 2.1. Historical and legislative features In the literature on the comparative study of national welfare states, the Italian social protection system is traditionally classified as belonging to the Bismarckian typology, typical of continental Europe, characterised mainly by a corporatist and fragmented structure of the various social assistance schemes, giving rise to substantial horizontal inequities among the various occupational and age groups of the population (Ferrera 1998). A number of empirical studies have recently laid emphasis on the defects which characterise the social assistance policies in Italy (Mantovani, Toso 1998; Marignetti, Roberti 1998, Rostagno, Utili 1998, Consolini, Donatiello 1999). The main shortcomings of the Italian system can be summarised as follows: • The lack of an overall regulatory law for the social assistance sector, from which many and strong differences in the benefits provided at local levels, both in kind and in cash, emerge. • An imbalance in the relative weight of cash transfers and in-kind services, with a strong predominance of the former ones. • The absence of a universal minimum income guarantee, as a temporary safety net for situations of particular need, administered at the national level. Many local authorities provide some forms of minimum income, but in a totally uncoordinated and discretionary way. • The dominant role played by categorical programs reserved to specific groups of citizens (elderly, invalids,…), identified on the basis of social or demographic characteristics which are only partially able to correctly detect situations of real economic need. • A consequent strong difference in the levels of protection guaranteed to different demographic and economic groups, in particular between the members of the regular and legal labour market (including those who have lost a job in the formal sector), pensioners, and invalids, on the one hand, and long-term unemployed, young people not yet enrolled in the labour market, and sick, on the other. • The mixture, in many schemes, of insurance and assistance elements, with respect to both the sources of financing and the eligibility criteria, with a resulting overlap between interpersonal and intra-personal, or life-cycle, redistribution objectives. • The very rudimentary nature of the criteria of means-testing, limited mainly to the taxable personal income of the head (sometimes extended to that of the partner), with great problems on the side of the correct identification of those in real need of assistance, and an extension on the expenditure side of public budget of the inequities produced by tax evasion. Equivalence scales are often used, although not always, but they differ between one scheme and the other, giving rise to substantial horizontal inequities. • The inadequacy of the monetary amounts of many transfers, generally insufficient to bring the beneficiary close to the poverty line. • The inefficiency of the public administration, and the consequent abuse of many institutes, in particular invalidity pensions and the partial contribution to medical expenses.
3 Many of the limits indicated are not a uniquely Italian phenomenon, but concern also the welfare states of other Mediterranean countries, which share some common socio-economic (late industrialisation, role of the family, structure of the labour market) and political characteristics (authoritarian experiences, ideological polarisation, strong presence of the Church in the field of assistance, subjection of the bureaucratic apparatus to the political power) (Ferrera 1996, Gough 1996). As a point of reference for the following discussion on the various assistance schemes, tab.1 summarises the level and disaggregation of the expenditure for social protection in 1997, trying to separate, among total social security outlays, the two basic components of “insurance” and “assistance” expenditures. Tab.1: Social protection expenditures in 1997 (billions of 1997 lire) 1997 % Pensions (social insurance) 248.145 % of Gdp 12,7 % of total social protection expenditures 56,3 Old age, seniority and invalidity pensions 283.145 - Supplementary pensions (estimates) - 32.000 - Early retirement benefits (estimates) - 3.000 Contributory outlays in the labour market (social insurance) 25.227 100,0 % of Gdp 1,3 % of total social protection expenditures 5,7 Unemployment and mobility allowances 6.110 24,2 Ordinary wage supplement 1.783 7,1 Disability and professional illness allowances 6.520 25,8 Temporary injuries and maternity allowances 5.504 21,8 Other contributory expenditures 2.310 9,2 + Early retirement benefits (estimates) 3.000 11,9 Social Assistance benefits 67.944 100,0 % of Gdp 3,5 % of total social protection expenditures 15,4 + Supplementary pensions (estimates) 32.000 47,1 Social pensions 3.609 5,3 Family allowances 7.237 10,7 Civil invalidity pensions 14.280 21,0 Blind or deaf pensions 1.726 2,5 Veteran pensions 2.625 3,9 Other transfers 6.467 9,5 Health 99.295 % of Gdp 5,1 % of total social protection expenditures 22,5 Total social protection outlays 440.611 % of Gdp 22,6 % of total public expenditures (excluding public debt repayment) 53,8 Source: Relazione Generale sulla Situazione Economica del Paese, 1997. In the empirical part of this paper we will focus on the distributive effects of many of the social assistance schemes listed in table 1, whose distinguishing features are here shortly reviewed: a) Family Allowance: it is a transfer reserved to households of dependent or ex-dependent workers with family burdens, and represent by far the main subsidy for households with dependent children. The amount of the transfer depends on the composition of the household and its income. The income test was introduced in 1983, and has emphasised the anti-poverty characteristics of this scheme, away from the original child benefit nature, universally granted.
4 b) Supplementary Pension: it is a benefit granted to old-age or invalid pensioners whose accrued pension is lower than a statutory minimum, about 8.5 million lire per year in 1998. The receipt of the subsidy is conditional on a test, introduced in 1983, on the taxable income of the potential beneficiary (plus that of the partner if married). The income test excludes non-taxable forms of income, e.g. capital incomes, and other items, such as imputed rents on owner-occupied house. The pension reform of 1995 has abolished this institute for the new entrants in the labour market, but it continues to apply for all other cases. c) Social Pension: it is a form of minimum income for people over 65 who are not entitled to a contributory pension, and thus neither to the supplementary pension. Its amount is around 6.5 million lire per year, and the receipt is subject to an income test of the single or of the couple, irrespective of the economic conditions of the household where one lives. In 1995 this scheme has changed its name into Social Allowance, but its main characteristics remain unaltered. d) INPS Invalidity Pension: like the two former programs, it is provided by INPS (Istituto Nazionale per la Previdenza Sociale), the institute responsible for the management of many contributory transfers, and is paid to workers with at least five years of contributions. Eligibility is conditional on both a medical visit and a test of income, and the accrued amount is supplemented to the minimum. Although formally a contributory scheme, this program should be more correctly considered as part of social assistance, because there is clear evidence, particularly during the ‘70s and ‘80s, of its misuse as a rough substitute for a missing universal safety net in preventing poverty, especially in the South and in non-industrialised areas. e) Civil Invalidity Pension: this scheme is very similar to the social pension (i.e. it is non contributory), but is reserved to the disabled without even a minimal accrued pensions. The income test is strictly individual, regardless the size of the family the beneficiary belongs to. f) Other social benefits: this is a residual category which includes, among others, the locally provided minimum incomes and the indemnity for persons accompanying the seriously disabled, a transfer provided without any form of means-testing. g) Unemployment Benefits: these are contributory benefits, but are considered here because it would otherwise be difficult to obtain a not misleading picture of the effects on poverty of the Italian cash transfers system. Note that those in irregular work and the young unemployed without previous work experience are not entitled to any form of assistance. 2.2 The recent debate and reform proposals 2.2.1 Towards a selective universalism From the data contained in table 1, the most distinguishing feature of the Italian cash transfer system clearly emerges: the dominant role of pensions as opposed to the residual role of assistance transfers. This has led many scholars to argue that social policy has come to be identified with pension policy, which absorbed also those spaces occupied in other welfare states by social assistance schemes. In general, the basic difference between “assistance” and “insurance” transfers should be found in the form of financing: contributions on earnings for insurance transfers, and general taxation for assistance schemes. The actual distinction is however particularly confused in the Italian case, where pensions have turned out to play also much of the antipoverty function which should conceptually reserved to social assistance schemes; typical are the cases of supplementary pensions, which fill the gap between a definite minimum and the accrued pension, clearly a form of assistance (as the reclassification of social expenditures in tab.1 reports), but reserved only to those pensioners with a minimum contributory record, and of family allowances, which have increased over time their poverty alleviation role, but are based on a contributory financing, and thus reserved only to that subset of the population which pays the social contributions. At a general level, these examples show that if a basically contributory system is requested to realise also antipoverty
5 objectives, strong differences in the levels of protection guaranteed to various population groups will inevitably emerge, producing substantial inequities. In the context of a categorical system, a move towards a more reliable and general test of means could represent an important and perhaps necessary pre-requisite for the extension of social assistance to parts of the population so far excluded or reached only with a distortionary use of existing schemes. Instead of producing the effect of rendering the welfare state more “residual”, a widespread use of consistent targeting methods can have the effect of allowing the system to become more universal and less fragmented. The problem of tax evasion can serve as an example to illustrate this point: tax evasion is mainly concentrated among specific sub-sectors of the labour force, particularly the self-employed and some dependent workers or early pensioners who can engage in a secondary activity. Though it is not the only reason, the diffusion of tax evasion contributes to explain why many components of the Italian social assistance system are categorical, and some exclude the self employed from the pool of beneficiaries (family allowances or unemployment benefits for example). A reform of the system towards universalism is thus not possible until new means testing criteria are introduced. In fact, using only the personal income tax base as means test would discriminate too much in favour of tax evaders, and amplify existing inequities. Two years ago, a special governmental commission (called Onofri Commission after the name of its co-ordinator: see Onofri Commission 1997) was set up to study the main deficiencies of the Italian welfare state and to suggest possible reform proposals. The work of this Commission stimulated a lively debate in the following months. Its basic message was the necessity to move towards a system able to associate universalism and selectivity: universalism in the potential access to the benefits, selectivity in the determination of the deserving households. To accomplish this program, the current system needs thus profound reforms both in the structure of the social protection schemes, and in the forms of the means-testing criteria. 2.2.2 A new targeting method: the Indicator of Economic Situation (ISE) The budget law for 1998 has fixed the guiding principles regarding the definition of general criteria for the evaluation of the economic means of persons applying for social assistance, in cash or in kind. These general principles have been clarified and made operative by a decree approved in March 1998, which has introduced the “Indicator of Economic Situation”, dubbed ISE (Indicatore della situazione economica). For a first experimental phase, whose time limits have defined just now (three years), the scope of the reform will apply only to social services and cash benefits provided at a local level (kindergartens, local forms of minimum income, nursing homes for the elderly,…). The previous test of means continue to apply to the old cash transfers provided by the central government, while also the newly adopted social assistance programs (a maternity leave for housekeepers and a family benefit reserved to poor families with at least three dependent children) will be subject to ISE. The spirit of the reform suggests that in the near future the whole welfare expenditure, both in kind and in cash, will be provided according the new targeting system. In brief, ISE will become the main instrument for the assessment of the economic conditions whenever a certain degree of selectivity is established, and will thus have important consequences on the distributive impact of the various forms of social protection. How ISE is defined. The new targeting instrument has two distinguishing characteristics: the economic condition is defined in terms of both income and wealth, and identifies in the household where one lives the appropriate unit of reference to determine the level of individual welfare, thus using an equivalence scale to deflate the sum of its income and wealth components, which can be defined in differentiated ways, according to their specific nature. More specifically, to the sum of all incomes of household members one must add the indicator of wealth position, given by the product
6 of total wealth by a coefficient α not greater than 0.2. Thus, ISE is a linear combination of income and wealth: ISE= (INCOME + α WEALTH) / EQ. SCALE The absence in the decree of a lower value for α implies that even 0 is an acceptable value; this would not violate the principle that requires to take account of wealth, since the income part includes also the flows of income from real and financial assets. The income component of ISE. The starting point is the total income relevant for the personal income tax, which is different from the personal income tax base since it includes also the social security contributions paid by the self employed (with rates of 15-16%), but not those paid by dependent workers. In this not very transparent way, the legislator has tried to allow for an important difference between these two categories of workers: the tax base for the employees is gross of the expenses necessary to produce it (later corrected by tax credits), while that of the self employed is net of these costs. Perhaps it would have been better to explicitly allow for a deduction from the employees’ tax base, or to consider directly not the tax base, but net income, which is closer to the concept of living standard, since it is difficult to consider the part of income which is paid in tax as part of any possible definition of living standard. However, it is reasonable to suspect that the reference to total income is due to the need to take account, in some way, of the grater propensity to evade the income tax by the self-employed: using total income instead of taxable income or net income, the ISE of the self employed is indeed augmented by 15%. The reference to a gross definition of resources is scarcely suitable to those programs aimed at alleviating poverty: for poor households, the appropriate concept of resources is disposable income, not only net of taxes, but also gross of other possible transfers from public administrations. The income part of ISE is obtained summing to total income a normal financial income, given by the application to the stock of financial assets of the average rate of long run Treasury bills. Income from real assets is already taken into account in the personal income tax base. From the value of income thus computed a deduction of 2.5 million lire (ca. 1300 euro) is allowed for tenants. The wealth component of ISE. The second component of ISE is given by the sum of the value of all real (houses, land,…) and financial assets. As for real estate, the relevant value is net of residual debts incurred for their purchase. Substantial disregards are provided: in general 50 million lire (26000 euro), increased to 70 mil. (36000 e.) if the household lives in its own house. In the choice of the means-testing indicator, the shift from an income-based measure to a new variable defined as a combination of income and wealth is the most important difference from the old Italian targeting system, and can be grounded on different alternative, theoretical or more practical, arguments. First of all, the majority of countries have targeting criteria which also use asset tests to select those eligible for social assistance (Eardley et al. 1996). Therefore, the adoption of ISE as a targeting instrument could be said to represent for Italy another step towards a more consistent and accepted framework for social assistance. From a theoretical point of view, ISE can be interpreted as a new measure of welfare only if one is willing to accept the idea that wealth increases utility in ways which are different and additional from the simple receipt of capital income from it. First of all, wealth ownership can enter the utility function directly, if its holding in itself generates additional utility, or indirectly (but equivalently), if it provides other benefits (sense of security, economic power and prestige, etc.) which are arguments of the utility function (Musgrave 1983, Carroll 1998). The utility function would thus be represented by U = U (Y, W) or U = U [Y, S(W)], where Y is income (earnings and capital income), W wealth, and S the services generated by the owning of wealth. According to this view, the autonomous role of wealth in generating utility does not imply a double counting of capital
7 income, even if a normal financial income, corresponding to an estimate of the annuity value of financial wealth, is already present in the income part of ISE. A further and independent conceptual justification for the direct introduction of wealth in ISE, which can also shed some light on the weight which should be attributed to it in a cardinal measure of welfare, deals with the length of time horizon of economic agents. If the time horizon of the typical agent is infinite, and we deny the validity of the former “security and prestige” argument, then the inclusion in ISE of both capital income and wealth would actually be an error of double counting. However, an infinite life is clearly an unreal situation, and if life is finite, then wealth gives to its owner, in excess of the flow of capital income, the possibility to bequeath it to his heirs, with a positive effect on his welfare. It should also be kept in mind that, if a person doesn’t have any descendants or is not interested in their utility, his wealth would still allow him to increase his own lifetime consumption in excess of the level guaranteed by capital income, through the liquidation of the asset. Ultimately, the ownership of a stock of wealth, which in principle survived the owner, is equivalent to an outward shift in the lifetime budget constraint. The parameter α in the expression of ISE should therefore reflect the optimal share of assets which in every period increases the consumption possibilities, and should thus depend on the interest rate and on the individual life expectancy, i.e. on his age (see Appendix 1 for a formal demonstration and some illustrative calculations). For our simulations, we have chosen two different values for the parameter α, applied to the real and financial components of wealth: 8% for the first one and 5% for the second. The text of the law is in fact sufficiently general to allow for the possibility that different parts of household wealth are treated with different criteria in the determination of ISE; in particular, it is implicitly possible to use distinct coefficients for real asset, on the one hand, and financial asset, on the other. The choice of these values has been done on the basis of both the formal argument presented in Appendix 1, and of the different evaluation methods used in ISE: market values for financial assets, and fiscal rents, substantially lower than market values, for real assets, so that it is more realistic to increase the coefficient for real wealth, even after taking into account its lower liquidity. If one is willing to accept the idea that wealth is in itself (directly or indirectly) part of the utility function, then ISE should not be used only as a means-testing device, but also as a cardinal measure of welfare, and therefore as the reference for the determination of the amount of transfer one is eligible to: cash transfers would subsidise not income, but welfare, whose level may be low only because its wealth part is particularly low. The practical consequences of this shift in perspective may however be lower than expected, since wealth is (particularly allowing for the presence of substantial disregards) a small part of ISE in its bottom deciles, as will be shown in the following section. Finally, to the theoretical justification for the direct inclusion of wealth in ISE, we must add a practical but significant one: tax evasion. Since ISE is still mainly based on taxable income, it cannot avoid the distortionary and unfair effects of income tax evasion, but the addition of wealth may partially correct for these distortions, if stock values are less subject to incorrect statements; moreover, stocks of wealth belonging to tax evaders can be interpreted at least in part as the result of the investment of unpaid taxes. The equivalence scale. A new equivalence scale has been introduced, necessary to compare the economic conditions of household of different composition. The scale is obtained simply by increasing to the power 0.65 the number of household components: ES = N 0.65 The elasticity of the scale to the number of members is thus constant, and equal to 0.65. The value lower than unity of the scale is obviously justified by the presence of economies of scale, while its constancy, instead of a declining value, could be motivated by the necessity for the household to
8 face substantial or extraordinary expenses when its dimensions increase, for example for the purchase of a new car, or the need to move to a bigger house. This basic scale is then increased when the household is in conditions of particular difficulty, by 0.2 points for single parent households with dependent children (still a rare typology in Italy), or if both parents of dependent children are working, and by 0.5 points for each member with a permanent handicap or seriously disabled. The choice of the form and values of the equivalence scale turned out to be a very delicate point during the debate which preceded the introduction of ISE: initially a scale with lower coefficients for children than for adults was suggested, on the basis of a rich empirical evidence stating that the cost of a child is lower that that of an adult, but the parliament rejected this proposal, arguing that the choice of a unique and common coefficient would protect the children, particularly in the light of the very low fertility rate of Italian women (about 1.2 children per woman), thus attributing to the equivalence scale an explicit normative content. Formal fulfilments and checks. Each person who wants to apply for social assistance must fill in a form containing all the previously described pieces of information regarding his economic conditions, and present it either to a centre of fiscal advice, or to the local authority or directly to the public administration office responsible for a particular intervention. With this declaration, the subject agrees also to the possibility that, if the benefit is allowed, the public administration may operate controls (with banks, other financial intermediaries, etc.) aimed at verifying the truthfulness of his statements. It is not difficult to foresee that, if these controls are credible, their threat can induce among tax evaders a reduction in the take-up rate for many services, thus contributing to limit the unfair consequences of tax evasion and fraud. The public administration, traditionally very inefficient, will thus be asked for a strong additional effort, on which much of the possibilities to improve the equity and efficiency characteristics of the system will depend. It is now time to summarise all these elements in a simple formula which details the content of our means-testing instrument: ISE = (Y+SEC+FY-R+α FW+β RW) / ES Where: Y: tax base of the personal and progressive income tax (Irpef) SEC: Social security contributions for self-employed workers FY: normal financial income, which in Italy is (almost wholly) not part of the Irpef tax base R: deduction for renters FW: Financial Wealth RW: Real Wealth α and β: coefficients comprised in the range 0-20% ES: Equivalence Scale Notice that the expression allows for the possibility to use differentiated coefficients for the two components of wealth, following the considerations made above. 2.2.3 A refinement of ISE as a measure of welfare: a proposal The new instrument for targeting social assistance expenditures presents some appreciable elements of novelty when contrasted with the previously used ones, based on the concept of personal taxable income. However, ISE as a welfare indicator still presents substantial limitations:
15 empty, while the top-right section, even if not densely populated, contains some observations: this means that a low ranking by taxable equivalent income may be associated with high levels of wealth, but low levels of wealth are never associated with the richest 50% of the income distribution. There are some households who are classified as poor or not particularly affluent in terms of taxable income, but who would see their ranking significantly changed according to the ISE, and would therefore be penalised by the new entitlement rules. The change in the welfare ranking, in the passage from income to ISE, could be influenced by many elements, such as the age of the household head, his job, and in particular by all those variables which are more strongly correlated with the owning of wealth. To analyse the specific contribution of each of a set of possible determinants, we performed a multinomial logit analysis, where households are divided into three groups: those whose decile rank falls in the passage from income to ISE, those who gain at least one decile, and those who do not change their decile, i.e. stay on the main diagonal (see Table 8). The comparison group is the set of households with a reduction in decile, i.e. that are poorer in terms of ISE, and the reference household has the following characteristics: it is resident in the north-western part of Italy, lives in its own house, and its head is a male, between 41 and 50 years old, white collar, and with at least 13 years of formal education. Tab.8: Multinomial logit model of Income - ISE decile mobility* 1) No change in decile 2) Increase in decile Coeff. tCoeff. t Age<31 -.282 -2.014 -.671 -3.360 Age 31-40 .042 0.435 -.157 -1.236 Age 51-60 .109 1.022 .199 1.489 Age 61-70 .232 1.696 .367 2.217 Age >70 .176 1.196 .702 4.031 Manual worker .179 1.679 .169 1.126 Manager .672 4.580 .123 0.551 Professional 1.859 7.429 2.883 10.432 Self employed 1.791 12.740 3.059 18.302 Pensioner from work .797 5.930 1.360 8.005 Pens. not from work 1.365 8.447 1.865 9.318 Unemployed 2.573 12.954 2.999 12.016 Other 1.681 8.736 2.519 10.493 Primary education -.1790 -1.879 -.144 -1.291 Secondary education -.1782 -2.019 -.183 -1.704 Degree 615 4.458 .223 1.232 North east .268 2.999 .692 6.771 Centre -.090 -1.018 .163 1.571 South -.0535 -0.685 -.609 -6.231 Female head -.223 -2.741 -.277 -2.801 Tenant -2.247 -31.186 -3.629 -28.236 N. comp. .118 2.744 .133 2.488 N. children 0-17 .117 1.950 .108 1.416 N. earners -.365 -7.455 -.668 -11.081 Constant .407 2.762 -.096 -0.501 * Reduction in decile is the comparison group Number of obs = 8135 Pseudo R2 = 0.1853 Log Likelihood = -7130.6571 Source: Dirimod95. The interpretation to be given to these results is, as partially anticipated, the following: those who increase their decile, i.e. are richer in terms of ISE, are more likely to lose the right to ask for social services, and in this sense are penalised by the shift from income to ISE. The results of the last two columns of tab. 8 show first that the probability to move from a lower level to a higher level of
16 welfare is consistently increasing with the age of the head, as a consequence of the process of wealth accumulation over the life cycle: ceteris paribus, the adoption of ISE should penalise households in the final part of their life, who on average have access to substantial stocks of wealth. Among the professional categories, independent workers make the biggest leap, followed by pensioners and the unemployed, who still remain in the bottom part of the distribution, but have levels of wealth which, however low, are greater than current income. The effect of education is low, perhaps since many of the elderly, who on average have substantial stock of wealth, have also low education levels. As for the geographic area, only those living in the North-East make a significant decile gain, while households living in the Southern part of Italy make an opposite leap. Female headship is associated with a decline in the ranking, as well as being tenants. Finally, the greater the number of earners, the bigger will be the reduction in decile from income to ISE: households with many earners are of course placed in the top part of the income distribution, but they may not be equally endowed with real or financial assets. The results of this analysis then imply that the likely “winners” from the adoption of ISE, in terms of a more favourable and easy access to social services, are households in the first stages of their life cycle, residents in the South, and with a dependent worker as the head. On the contrary, the “losers” will be households with a head not employed as dependent worker (particularly the selfemployed), more than 60 years old, resident in the North-eastern part of Italy. The two alternative classification systems are further contrasted in the following table, showing how many households would change their position in the passage form income to ISE (see Table 9). If we make the simplifying assumption that poor households in terms of equivalent income are the beneficiaries of current welfare services, while ISE is actually the most consistent targeting criterion, nearly 16% of households (3.5% / 22%) who are poor in terms of income would not be classified as ISE poor, and thus would lose access to social assistance; these households can be termed false positives, since only the adoption of an unsatisfactory targeting criterion allows them to belong to the pool of the beneficiaries of social assistance. On the other hand, 7.1% of the sample are not poor in terms of income, but should be entitled to welfare transfers according to ISE, and therefore are false negatives in terms of income. Tab.9: Poor households in terms of personal taxable income or ISE Poor in terms of ISE No Yes Poor in terms of taxable equivalent income No True negatives 70.9% Area D False negatives 7.1% Area B 78% Yes False positives 3.5% Area C True positives 18.5% Area A 22% 74.4% 25.6% 100% Source: Dirimod95. The four groups a household can belong to are shown graphically in Fig.2, where W is wealth and Y income. The vertical line is the poverty line in terms of income, while the other segment represents the ISE poverty line, with a slope of –1/α, and thus areas A and C identify the income poor, and areas A and B the ISE poor. Those belonging to area B would thus be favoured by the adoption of ISE, and those in area C would be penalised. Some probit analyses conducted on the probability to belong to each of these areas, whose results are not reported for brevity (see Baldini et al. 1999), have shown that the probability to fall in the B area is particularly high for those households with a low educational level, resident in the Central or Southern regions of Italy, with a female head and living in a rented house. Conversely, the probability of falling in area C is high especially for households with a self-employed head. This analysis confirms the former multinomial
17 logit regression analysis, and also completes it since it is concentrated only on those households making big leaps across the two distributions. Fig.2: Winners and losers in the passage from the income to the ISE distribution 4. Towards a new framework for social assistance The introduction of ISE is going to have important implications not only for the selection of the beneficiaries of cash or in kind transfers, but can, at least in principle, provide the basis for a deep restructuring of the whole system of social assistance. As already discussed, the adoption of a new means-testing criterion is one of the main innovations that the Italian welfare spending system has recently implemented in order to satisfy the twofold objective of the Onofri Commission, namely a broad universalism, in terms of categorical eligibility to the benefits, and a more efficient degree of selectivity in the determination of the deserving households. However it should be stressed that only with profound changes in its institutional structure, the current system, which is still characterised by a number of categorical schemes, is likely to approach the universal vision envisaged by the legislator. Some first steps towards the extension of the pool of potential beneficiaries have recently been made. In particular in the last 12 months three new schemes have been introduced, which represent also the first concrete applications of ISE: a) A Special Family Allowance of 2.6 million lire per year (1350 euro) for households with at least three dependent children, and with an ISE lower than 30.8 million for a reference household with 5 members (other thresholds are derived with the ISE equivalence scale). The amount of the subsidy is still positive although decreasing with a withdrawal rate of 50% up to the ceiling of 36 million lire (the cut-out point). Total spending for 1999 is estimated in 390 billion lire. b) A Maternity Allowance of 1 million lire (516 euro) for each new child, granted if ISE is lower than 50 million lire for a reference household of three members, and if the mother is not covered by any forms of maternity insurance. Total estimated spending is 25 billion lire per year. c) The Minimum Insertion Income (Reddito Minimo di Inserimento, in brief RMI), which represents a first but significant step towards the adoption in Italy of a universal subsidy for the alleviation of poverty, modelled on the basis of the safety nets present in almost all European countries. In a first and experimental phase of three years, the RMI will be introduced only in 42 local areas (among them Napoli, Catania, Genova, Reggio Calabria), chosen according to a complex set of social and economic characteristics, and mainly concentrated in the southern part of Italy, the poorest one. The maximum amount of the RMI is 0.5 million lire (260 Euro) per month for a single person, while for other households the corresponding amounts are found with A: 18.5% B: 7.1% D: 70.9% C: 3.5% W Y Income poverty line ISE poverty line
18 the application of the ISE equivalence scale. The transfer is set so as to cover the difference between the maximum amount and household income. Earnings are counted in total household income only for 75% of their total amount, to attenuate the "poverty trap", so that the RMI reproduces a negative income tax scheme with a marginal tax rate of 0.75, covering a constant share of the poverty gap (the difference between the threshold and household income). The entitlement rules for the RMI do not adopt ISE as a selection instrument or as a measure of living standard, even if they share with the ISE legislation the same equivalence scale and the adoption of the household as the resource unit. It is important to notice that any amount of assets, however small, is a sufficient condition for losing eligibility. This pre-requisite appears to be coherent with the nature of the scheme, aimed at alleviating situations of particularly harsh poverty and social exclusion. The receipt of the minimum income is conditional on joining an insertion program, devised by the local authorities with the objective of reintroducing the beneficiary in the labour market, through the acceptance of any job proposals, the attendance of training courses, or the involvement in care services. As far as this measure is extended to the whole population, first provisional estimates show that the RMI will cost about 10.000 billion lire per year. These three schemes, and in particular the RMI, have the purpose of rendering less categorical the Italian welfare state, in the sense of including in the pool of beneficiaries parts of the population so far excluded, notwithstanding their economic conditions; if and when the RMI passes the experimental phase, Italy will have a universal scheme of poverty alleviation, with the RMI (or perhaps a revised version of it) for the non elderly and the social pension for the over-65. The distributive effects of the new regime are not clear, and depend also on the gradual corrections or on phasing-out of old schemes (especially INPS invalidity pensions and old-age supplementary pensions) and on the nature of the new ones; more specifically, if a new means-testing criterion manages to correct the defects of previous targeting instruments, then new and less categorical expenditure programs can be introduced, and those who appear to be penalised by the new means test can actually turn out to become eligible to new forms of assistance to which they were previously excluded. We have already noted that many categories, e.g. the self-employed or the young unemployed who have never worked, still lack access to substantial cash transfers if they are in need or have family burdens, but these evident inequities, justified on many grounds (tax evasion, incentive effects, contributory financing,…) could be at least partially overcome if a new and more efficient management of the spending system is introduced. ISE is only a part of the necessary reforms, which must include also a reformulation of policies to reintroduce to work those living on welfare subsidies, a strong improvement in the efficiency of the administrative structure, and the strengthening of the control procedures, but it can contribute to create the ideal conditions for a structural reform of the system. As reported in section 2, the final coverage of ISE is still not clear, in particular whether or not it will be applied also to the selection of beneficiaries of existing cash transfers. As a preliminary step towards a more comprehensive reform of social assistance policies, it may be interesting to check the consequences of a simple experiment, i.e. the application of ISE to the current cash benefits simply as an entitlement criterion, or at least to those benefits who are explicitly aimed at fighting poverty or which have been de facto used with this purpose. Table 10 reports first the share of total expenditure for each scheme going to those households placed below the poverty line computed on ISE without the relevant scheme (that is, the poverty line changes for each row); the second column shows the percentage of current beneficiaries of each subsidy who are not poor in terms of the same variable, and who therefore would lose the transfer if ISE were applied and poverty alleviation were the only aim of the scheme. The last two columns report the same values, but for poverty lines defined in terms of net equivalent income. The results, partly anticipated by the section on efficiency and effectiveness of social transfers, are striking: in the case of supplementary pensions, for example, 57.7% of the beneficiaries are households whose
19 ISE (before the benefit itself) is greater than the poverty line, and the same is true for 41.3% of households of social pensioners. These percentages are magnified if the poverty line is in terms on disposable income, since the poverty level is lower. The new programs (RMI, the Special Family Allowance, and the Maternity Allowance) are not surprisingly much more concentrated towards the poor. Tab. 10: ISE as a selection mechanism for current programs Share of total expenditure going to ISE poor % of current beneficiaries who are not ISE poor Share of total expenditure going to income poor % of current beneficiaries who are not income poor Supplementary pensions 41.8 57.7 33.8 67.7 Social pensions 60.5 41.3 38.3 63.4 Civil Inval. pensions 48.1 52.4 32.6 71.8 INPS Inval. pensions 50.9 49.7 48.6 55.7 Minimum insertion income 98.5 2.4 96.7 5.7 Special family allowance 100.0 0.0 86.7 17.3 Maternity allowance 71.8 28.2 35.6 64.4 Source: Dirimod95. The amount of redistribution that would be implied by the adoption of ISE, simply as a threshold to target the pool of beneficiaries, seems therefore so pervasive to become politically impracticable in the short run, because it would imply an excessive reshuffling of vested rights. It thus becomes more interesting, if not more realistic, to imagine a completely new spending structure, which will very gradually substitute the old transfers, and can be characterised, in a very hypothetical way, by only two instruments in place of the many seen so far: a) A Child Allowance, giving the same total expenditure of current family benefits, but less concentrated on poor households: it would lose part of the anti-poverty objective implicit in its current structure, being however still more generous with non affluent households. b) A Minimum Income Guarantee, which could cover the whole or part of the ISE poverty gap. We test here the distributive implications of the introduction of the new programs quoted before (the RMI, the Special Family Allowance, and the Maternity Allowance), and of the completely new system just mentioned (the Child allowance and the Minimum Income Guarantee); this last simulation is of course highly speculative, but can shed some light on the likely direction towards which the welfare state is evolving if it wants to overcome its main limitations. As for the formal specification of the two new schemes, we adopt the following structure for the Child Allowance (CA): CA = K NCH0.65 if ISE < ISEmin K NCH0.65 [(ISEmax-ISE) / (ISEmax-ISEmin)] if ISEmin < ISE < ISEmax 0 if ISE > ISEmax where K is the amount which realises the requisite of equal expenditure with the current family allowance, and turns out to be about 2 million lire (1030 euro) per year, NCH is the number of children between 0 and 17 years old, ISEmin is the threshold between the second and third decile of the ISE distribution, and ISEmax is the corresponding value at the top of the eighth decile. The Child Allowance is given in its full amount to those belonging to the first two deciles of ISE, it is not given at all to the richest 20%, and decreases proportionally in the intermediate deciles, according to the level of ISE. The extension of this scheme to the majority of households should restore its original nature of child subsidy, and should also reduce the disincentive effects on female labour supply. The Minimum Income Guarantee has been simulated in two different forms: a) MIG1: total filling up of the ISE poverty gap, without budgetary constraints.
20 b) MIG2: partial filling up of the ISE poverty gap, 50% for those households with an head less than 65 years old, and 80% for others, so as to produce the same total expenditure as the current welfare programs (excluding temporary unemployment benefits, which survive). The results in terms of the distribution of ISENET are shown in table 11. “Current Benefits” represent the sum of all benefits currently present, while the “New schemes” summarises the three programs quoted before (the RMI, Additional Family Allowance, and the Maternity Allowance). “New benefits 1” is the sum of the Child Allowance and the first version of the Minimum Income Guarantee (MIG1), which implies a total coverage of the ISE poverty gap, while “New benefits 2” includes the Minimum Income Guarantee in its second version, MIG2, which closes the ISE poverty gap only partially. The effect of current benefits in reducing inequality is substantial, as can be seen by the reduction of 2.5 points in the Gini index. Such a reduction appears to be particularly significant since ISENET contains also an asset component which, as already seen, is very unequally distributed. Few households exit from poverty thanks to current benefits, but the poverty gap ratio (with endogenous (new) poverty line) is reduced by a quarter. "New schemes" does not have a very high aggregate impact, essentially because its total expenditure is very low as already indicated, and the RMI has the great drawback of excluding those households who own even a small amount of financial or real assets (with the exception of the house of residence): this restricts significantly the potential pool of beneficiaries, and could induce undesirable distortionary effects on saving behaviour, so some disregards on financial assets could be advisable. The hypothetical new welfare system is of course much more effective in fighting poverty: in particular its second version, more realistic, induces a limited fall in the percentage of households in poverty, but a sharp drop in the poverty gap ratio, without increasing its cost with respect to the current regime. Tab.11: Distributive effects of total benefits Gini index Head count ratio Poverty gap ratio ISENET without current benefitsa0.417 0.236 0.407 ISENET + Current benefits 0.392 0.210 0.324 ISENET + Current benefits + New schemes b 0.389 0.208 0.306 ISENET + New benefits 1c0.349 0.076 0.046 ISENET + New benefits 2 d 0.371 0.170 0.161 (a) Sum of all benefits of the current system (see par. 2.1) (b) Special Family Allowance, Maternity Allowance, RMI. (c) Child Allowance and MIG1 (d) Child Allowance and MIG2 Source: Dirimod95. Table 12 shows that the recent measures improve significantly all the efficiency and effectiveness indicators. The new Child Allowance is less concentrated on poor households than the current one (the VEE falls by ten points if compared with the figure of Family Allowances in Table 5), while by definition the concentration on poor households is extreme for both versions of the MIG. Tab.12: Efficiency and effectiveness of social welfare expenditure VEE PRE SPGE Current benefits 44.93 37.04 17.57 34.81 Current benefits + New schemess 48.24 40.58 15.88 39.84 Child Allowance 48.07 45.34 5.69 7.21 MIG1 96.44 75.27 21.95 96.89 MIG2 96.17 86.23 10.34 70.88 New Benefits 1 90.00 67.26 25.25 99.31 New Benefits 2 86.43 77.19 10.69 77.47 Source: Dirimod95.
21 At this point, it is possible to extend the analysis started in the previous section, and ask who is going to gain and to lose not only from the introduction of ISE, but also from a different, simpler and more universal set of cash transfers. We concentrate here on two classificatory variables, the profession of the head and his age class. The first column of table 13 reports the share of each group in the total population, and the second the share of total ISENET computed without benefits; the manual workers, pensioners not from work, the unemployed and others own a lower part of total ISENET than their share in the population, so they are relatively less well off than other groups. These are the same groups for which, consistently with the purpose of a redistributive system of cash transfers, the share of current benefits they receive is greater than their share of ISENET, with the exception of pensioners from work, who therefore appear to be overprotected. The introduction of the three recent welfare schemes, and particularly of the RMI (when it will be extended to the whole population), produces an increase in the amount of resources going in favour of the independent workers (who now lack any form of child benefit and unemployment subsidy) and the unemployed, reducing the expenditure towards pensioners. Tab.13: Distributive effects of total benefits by demographic groups Share of total population Share of total ISENET without benefits Share of current benefits Share of current benefits + New schemes Share of New Benefits 2 % reduction in poverty with current benefits % reduction in poverty with New benefits 2 Profession of the head Manual worker 17.6 12.7 16.5 16.4 19.0 -17.1 -27.7 White collar 13.6 15.6 6.3 6.0 5.2 -14.2 -26.2 Manager 4.9 8.7 1.3 1.2 0.5 -6.1 -16.7 Professional 2.9 6.5 0.2 0.4 0.5 -2.3 -32.6 Self employed 11.2 12.3 4.2 5.2 9.2 -4.4 -24.2 Pensioner from work 31.2 33.2 39.3 36.9 24.7 -25.2 -59.2 Pens. not from work 10.3 6.6 21.5 20.3 21.7 -22.0 -46.6 Unemployed 3.9 1.4 7.0 9.3 13.6 -6.6 -20.2 Other 3.6 3.0 3.6 4.1 5.5 -5.7 -11.5 Total 100 100 100 100 100 -17.0 -38.2 Age of the head <=30 5.4 4.7 3.5 4.3 5.8 -6.1 -21.0 31-45 28.1 26.4 20.6 22.8 32.7 -12.7 -26.3 46-60 30.2 33.0 22.2 22.5 20.0 -12.3 -20.4 61-70 18.6 19.8 26.3 24.8 18.1 -24.7 -49.8 >70 17.7 16.1 27.4 25.6 23.3 -23.8 -64.4 Total 100 100 100 100 100 -17.0 -38.2 Source: Dirimod95. It is particularly interesting that the scenario New Benefits 2 shows the same picture of the scenario New schemes, as far as the redistribution of resources among groups is concerned, although obviously in much more extreme terms: independent workers and the unemployed (but now also manual workers, who have relatively low ISE and many children) gain in share, while pensioners lose. In any case, this does not imply a worsening of the performance of the system in preserving pensioners from poverty, since, as can be seen from the last two columns, the percentage reduction in poverty, starting from the distribution of ISENET without benefits, is with the new system greater for all groups (even if total estimated expenditure is the same), and particularly so for pensioners, even if their relative share of total transfers has been reduced. The reason for this result lies in the great amount of resources that is now wasted being directed towards households not in
22 actual conditions of need. The values of the percent reductions are also more uniform, and this is a sign of the move towards a less categorical system2. The same reasoning can be repeated with respect to the age classification; both in the case of the new three welfare schemes ("New schemes") and in the simulation called New Benefit 2 there is an increase in the share of total benefits going towards the first three age classes and a reduction for the oldest two, but the reduction in poverty is still greater for these last age brackets. 5. Conclusions The Italian public assistance system is currently interested by an intense process of reform, aimed at overcoming its main limitations, in particular its basic categorical nature and the rudimentary nature of test of means applied to current spending schemes. This process should lead to a model of welfare state able to realise a greater universalism, while satisfying the public budget limitations. The reform perspective envisaged by the legislator can be labelled as one of “selective universalism”. In this paper we have studied the distributive effects that are likely to emerge from the revision of the criteria used to test the economic conditions of the beneficiaries, now suffering from great inconsistencies, elements of irrationality and an insufficient ability to direct public expenditure towards those most in need. The main points raised and the conclusions reached in the paper can be summarised as follows: 1) Our empirical analysis confirms the strongly negative distributive performance, already noted in other works, of social assistance expenditure in Italy, both in efficiency and effectiveness terms; there is thus much scope for a better targeting of current welfare expenditure in favour of those truly regarded as being in need, without violating the currently tight budget constraints. 2) The recent replacement of the plethora of means test previously in use, based on individual taxable income of potential beneficiaries, with a new system of means-testing (ISE), based on a joint test of asset and income of the household of the beneficiary appears to play a crucial role in the process of reform of social assistance policies in Italy. The new test of means should in fact guarantee a more uniform and equitable targeting of welfare expenditure, in a general context of fiscal restraint. A further measure of beneficiaries' welfare, called ISENET, is proposed here, as a refinement of ISE. 3) A comparative analysis of the distributive profiles of the old and new means-testing criteria, in order to evaluate how different economic and demographic groups of the population are likely to change their relative position if households are ranked first by a variable representing old means tests and then by ISE, shows that the likely “winners” from the adoption of ISE, in terms of a more favourable entitlement to social services, are households in the first stages of their life cycle, residents in the South, and with a dependent worker as the head. On the contrary, the “losers” will be households with a head not employed as dependent worker (particularly the self-employed), more than 60 years old, resident in the North-eastern part of Italy. 4) The amount of horizontal redistribution associated with the adoption of ISE, simply as a threshold for the eligibility to the existing benefits, seems so pervasive to become politically impracticable in the short run, because it would imply an excessive reshuffling of vested rights. Therefore we focused on a completely new spending structure, which would very gradually substitute the old transfers, and can be characterised, in a very hypothetical way, by only two schemes, in place of the many currently at work: a Child Allowance, costing the same total amount of current family benefits, but less concentrated on poor households, and a Minimum Income Guarantee, which could cover the whole (or part of the) ISE poverty gap. More precisely, we tested the distributive implications of the recently introduced programs (the 2 The penultimate column of Table 13 is taken from Table 6, column d).
23 Special Family Allowance, the Maternity Allowance, the Minimum Insertion Income), and of the new scenario before mentioned (Child Allowance plus a Minimum Income Guarantee). The latter simulation has been of course highly speculative, but sheds some light on the likely direction towards which the Italian social assistance system is evolving if it wants to overcome its main limitations. 5) The completely reformed system with a partial coverage of the ISE poverty gap ("New benefits 2") shows a distributive impact which, in qualitative terms, is quite similar to that one shown by the three new programs, recently introduced (the Special Family Allowance, the Maternity Allowance, the Minimum Insertion Income): independent workers and the unemployed (but also manual workers, who have relatively low ISE and many children) would gain in share, while pensioners lose. In any case, this wouldn't imply a worsening of the performance of the system in preserving pensioners from poverty, since the percentage reduction in poverty, starting from the distribution of ISENET without benefits, is greater for all groups in the new system (even if total estimated expenditure is the same), and particularly so for pensioners, even if their relative share of total transfers has been reduced. The reason for this result is due to the fact that the great amount of resources that is now wasted would be directed towards households not in actual conditions of need.
24 Appendix 1: Determination of wealth coefficients in ISE and the time horizon of beneficiaries We show here the simple formulas that allow to determine the constant rate of decumulation of a stock of wealth, if the agent owns an asset which produces R as the annual flow of income. If the agent lives forever, or is interested in the utility of his descendants, the value of the stock of wealth is given by W = R/r where r is the interest rate; if his time horizon is finite, the capitalised value of the finite flow of future incomes is W = (R/r) [1-1/(1+r)n] = Rτ/r if τ = 1-1/(1+r)n then R = Wr/τ = Wα’ so the coefficient α’ depends both on the interest rate and on the residual life span. The value for R thus determined, however, contains both capital income and the premium associated to the possibility of disposing of a stock of wealth; if we want to define α’ so as to be consistent with the introduction of capital income in the income component of ISE, we should deduct from α’ the interest rate, representing the flow of normal capital income for each unit of wealth: α = α’ - r = r/τ - r = r / [(1+r)n-1] The coefficient multiplying wealth in the ISE definition, α, is a decreasing function of both r (the higher the interest rate, the lower is the value of future income streams) and n (the younger the agent (high n), the lower is the constant share of wealth that can be depleted in each year). If for example, r=5% and n=10, then α=8%, if r=5% and n=20, then α=3%, if r=5% and n=5, then α=18%. We do not completely follow these result, however, since in the simulations presented in the main text α is a constant, independent of the age of the person, because the use of a coefficient variable with age may perhaps be appropriate for some specific assistance schemes (e.g. nursing homes), but its generalised application would be too penalising for the elderly.